Outperformance and Tracking : Dynamic Asset Allocation for Active and Passive Portfolio Management

29 Pages Posted: 31 Jan 2017 Last revised: 19 Mar 2018

See all articles by Ali Al-Aradi

Ali Al-Aradi

University of Toronto - Department of Statistics

Sebastian Jaimungal

University of Toronto - Department of Statistics

Date Written: January 30, 2017

Abstract

Portfolio management problems are often divided into two types: active and passive, where the objective is to outperform and track a preselected benchmark, respectively. Here, we formulate and solve a dynamic asset allocation problem that combines these two objectives in a unified framework. We look to maximize the expected growth rate differential between the wealth of the investor's portfolio and that of a \textit{performance} benchmark while penalizing risk-weighted deviations from a given \textit{tracking} portfolio. Using stochastic control techniques, we provide explicit closed-form expressions for the optimal allocation and we show how the optimal strategy can be related to the growth optimal portfolio. The admissible benchmarks encompass the class of functionally generated portfolios (FGPs), which include the market portfolio, as the only requirement is that they depend only on the prevailing asset values. The passive component of the problem allows the investor to leverage the relative arbitrage properties of certain FGPs and achieve outperformance in a risk-adjusted sense without requiring the difficult task of estimating of asset growth rates. Finally, some numerical experiments are presented to illustrate the risk-reward profile of the optimal allocation.

Keywords: Active portfolio management, Stochastic Portfolio Theory, Portfolio Optimization, Stochastic Control, Growth Optimal Portfolio, Functionally Generated Portfolios

Suggested Citation

Al-Aradi, Ali and Jaimungal, Sebastian, Outperformance and Tracking : Dynamic Asset Allocation for Active and Passive Portfolio Management (January 30, 2017). Available at SSRN: https://ssrn.com/abstract=2908552 or http://dx.doi.org/10.2139/ssrn.2908552

Ali Al-Aradi

University of Toronto - Department of Statistics ( email )

100 St. George St.
Toronto, Ontario M5S 3G3
Canada

Sebastian Jaimungal (Contact Author)

University of Toronto - Department of Statistics ( email )

100 St. George St.
Toronto, Ontario M5S 3G3
Canada

HOME PAGE: http://www.utstat.utoronto.ca/sjaimung

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